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Leya [2.2K]
3 years ago
15

Given points (r1, u1 ) and (r2, u2) in polar coordinates, obtain a general formula for the distance between them. Simplify it as

much as possible using the identity cos2 u 1 sin2 u 5 1. Hint: Write the expressions for the two points in Cartesian coordinates and substitute into the usual distance formula.
Mathematics
1 answer:
sertanlavr [38]3 years ago
6 0

Answer:

  d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}

Step-by-step explanation:

The Law of Cosines gives an immediate result. No translation to Cartesian coordinates is necessary. That law makes use of the angle between the vectors, u2-u1

  d^2=r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)\\\\\boxed{d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}}

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Chisaka has less than 145kg of food remaining in her spaceship. She needs a constant amount of food each day that she spacewalks
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If Chisaka does not space walks, the days she spend spacewalking are equal to zero. Since <span>S represents the number of days Chisaka spacewalks, we just need to replace </span>S=0 in our inequality to find how long her food will last if she does not spacewalks:
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4 years ago
What is the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings
Sophie [7]

Answer:

the experimental probability is 70%

Step-by-step explanation:

PLEASE HELP, TIMEDThe table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have.

What is the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings?

To the nearest whole percent, the experimental probability is

a. 65%.

b. 70%

c. 75%

d. 80%

We are given to find

the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings

we know that

probability = ( number of favourable outcomes)/ ( total possible outcomes)

a 10th-grade student chosen at random has at least one, but no more than two, siblings

so, there can be one or two siblings

so, total number of such students =18+10=28

Number of favourable outcomes =28

total number of students =4+18+10+8=40

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p=\frac{28}{40}\\\\p=\frac{28}{40}\times 100\\\\p=70

So,

Therefore, the experimental probability is 70%

7 0
3 years ago
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